Why we should love logarithms – nature.com
The notion of a decreasing distance between numbers makes perfect sense once we think about that difference in proportionate terms: 1,001 is clearly more akin to 1,000 than 2 is to 1. We can even quantify those degrees of likeness. If we space numbers along a scale such that the distances between them reflect the proportion by which they increment the previous number, then the distance of a number n from 1 is given by the harmonic series, the sum of 1 + 1/2 + 1/3 + 1/4 and so on up to 1/n. This distance is roughly proportional to the logarithm of n.
This, it is often said, is why life seems to speed up as we get older: each passing year is a smaller proportion of our whole life. In perceptual terms, the clock ticks with an ever faster beat.
Love your logs.